Abstract Propagation of acoustic waves is considered in a system consisting of two stiff quarter-spaces connected by a planar soft layer. The two quarter-spaces and the layer form a half-space with a planar surface. In a numerical study, surface waves have been found and analyzed in this system with displacements that are localized not only at the surface, but also in the soft layer. In addition to the semi-analytical finite element method, an alternative approach based on an expansion of the displacement field in a double series of Laguerre functions and Legendre polynomials has been applied. It is shown that a number of branches of the mode spectrum can be interpreted and remarkably well described by perturbation theory, where the zero-order modes are the wedge waves guided at a rectangular edge of the stiff quarter-spaces or waves guided at the edge of a soft plate with rigid surfaces. For elastic moduli and densities corresponding to the material combination PMMA-silicone-PMMA, at least one of the branches in the dispersion relation of surface waves trapped in the soft layer exhibits a zero-group velocity point. Potential applications of these 1D guided surface waves in non-destructive evaluation are discussed.

中文翻译：

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表面声波局限于两个刚性弹性四分之一空间之间的软层

摘要 声波的传播被考虑在一个由两个刚性四分之一空间组成的系统中，该系统由一个平面软层连接。两个四分之一空间和层形成一个具有平面表面的半空间。在数值研究中，已经在该系统中发现并分析了表面波，其位移不仅位于表面，而且位于软层中。除了半解析有限元方法之外，还应用了一种基于拉盖尔函数和勒让德多项式双级数中位移场扩展的替代方法。结果表明，模态谱的许多分支可以被微扰理论解释和很好地描述，其中零阶模式是在刚性四分之一空间的矩形边缘引导的楔形波或在具有刚性表面的软板边缘引导的波。对于PMMA-硅胶-PMMA的材料组合对应的弹性模量和密度，在软层中捕获的表面波色散关系中的至少一个分支表现出零群速度点。讨论了这些一维引导表面波在无损评估中的潜在应用。